MSDS 6372 Project 1 Objective 2
Jaclyn A Coate
1/22/2020
library(tidyverse)
library(mice)
library(skimr)
library(corrplot)
library(car)
library(ISLR)
library(ggplot2)
library(gridExtra)
library(SamplingStrata)
library(rbin)
library(leaps)
library(dplyr)
library(ggplot2)
library(geosphere)
library(broom)
library(plyr)
library(devtools)
options(scipen=999)Objective 2 EDA:
nycraw <- read.csv("https://raw.githubusercontent.com/JaclynCoate/6372_Project/master/AB_NYC_2019.csv", header = TRUE, strip.white=TRUE)
head(nycraw)## id name host_id
## 1 2539 Clean & quiet apt home by the park 2787
## 2 2595 Skylit Midtown Castle 2845
## 3 3831 Cozy Entire Floor of Brownstone 4869
## 4 5022 Entire Apt: Spacious Studio/Loft by central park 7192
## 5 5099 Large Cozy 1 BR Apartment In Midtown East 7322
## 6 5121 BlissArtsSpace! 7356
## host_name neighbourhood_group neighbourhood latitude longitude
## 1 John Brooklyn Kensington 40.64749 -73.97237
## 2 Jennifer Manhattan Midtown 40.75362 -73.98377
## 3 LisaRoxanne Brooklyn Clinton Hill 40.68514 -73.95976
## 4 Laura Manhattan East Harlem 40.79851 -73.94399
## 5 Chris Manhattan Murray Hill 40.74767 -73.97500
## 6 Garon Brooklyn Bedford-Stuyvesant 40.68688 -73.95596
## room_type price minimum_nights number_of_reviews last_review
## 1 Private room 149 1 9 10/19/18
## 2 Entire home/apt 225 1 45 5/21/19
## 3 Entire home/apt 89 1 270 7/5/19
## 4 Entire home/apt 80 10 9 11/19/18
## 5 Entire home/apt 200 3 74 6/22/19
## 6 Private room 60 45 49 10/5/17
## reviews_per_month calculated_host_listings_count availability_365
## 1 0.21 6 365
## 2 0.38 2 355
## 3 4.64 1 194
## 4 0.10 1 0
## 5 0.59 1 129
## 6 0.40 1 0str(nycraw)## 'data.frame': 34464 obs. of 16 variables:
## $ id : int 2539 2595 3831 5022 5099 5121 5178 5203 5238 5295 ...
## $ name : Factor w/ 34000 levels ""," Private 1 bdrm Lefferts Gr, BK apt",..: 8990 27105 11178 13776 17775 5839 17808 11099 12643 3931 ...
## $ host_id : int 2787 2845 4869 7192 7322 7356 8967 7490 7549 7702 ...
## $ host_name : Factor w/ 9124 levels ""," Valéria",..: 4017 3840 4984 4754 1544 2840 7735 5519 958 4836 ...
## $ neighbourhood_group : Factor w/ 5 levels "Bronx","Brooklyn",..: 2 3 2 3 3 2 3 3 3 3 ...
## $ neighbourhood : Factor w/ 218 levels "Allerton","Arden Heights",..: 108 127 42 62 137 14 95 201 36 201 ...
## $ latitude : num 40.6 40.8 40.7 40.8 40.7 ...
## $ longitude : num -74 -74 -74 -73.9 -74 ...
## $ room_type : Factor w/ 3 levels "Entire home/apt",..: 2 1 1 1 1 2 2 2 1 1 ...
## $ price : int 149 225 89 80 200 60 79 79 150 135 ...
## $ minimum_nights : int 1 1 1 10 3 45 2 2 1 5 ...
## $ number_of_reviews : int 9 45 270 9 74 49 430 118 160 53 ...
## $ last_review : Factor w/ 908 levels "1/1/17","1/1/18",..: 113 575 775 175 671 144 677 745 716 671 ...
## $ reviews_per_month : num 0.21 0.38 4.64 0.1 0.59 0.4 3.47 0.99 1.33 0.43 ...
## $ calculated_host_listings_count: int 6 2 1 1 1 1 1 1 4 1 ...
## $ availability_365 : int 365 355 194 0 129 0 220 0 188 6 ...nrow(nycraw)## [1] 34464EDA to determine type of multiple linear regression to perform
Determined that Times Square is a hot destination point. Used Lat long metrics to build a new metric with distance to Times Square
#Creating a new, tsquare_distance (distance to Times Square in miles)
for (i in 1:nrow(nycraw)) {
n <- (distHaversine(c(nycraw$latitude[i], -nycraw$longitude[i]), c(40.7580, 73.9855)) / 1609.344)
nycraw$tsquare_distance[i] <- n
}
head(nycraw)## id name host_id
## 1 2539 Clean & quiet apt home by the park 2787
## 2 2595 Skylit Midtown Castle 2845
## 3 3831 Cozy Entire Floor of Brownstone 4869
## 4 5022 Entire Apt: Spacious Studio/Loft by central park 7192
## 5 5099 Large Cozy 1 BR Apartment In Midtown East 7322
## 6 5121 BlissArtsSpace! 7356
## host_name neighbourhood_group neighbourhood latitude longitude
## 1 John Brooklyn Kensington 40.64749 -73.97237
## 2 Jennifer Manhattan Midtown 40.75362 -73.98377
## 3 LisaRoxanne Brooklyn Clinton Hill 40.68514 -73.95976
## 4 Laura Manhattan East Harlem 40.79851 -73.94399
## 5 Chris Manhattan Murray Hill 40.74767 -73.97500
## 6 Garon Brooklyn Bedford-Stuyvesant 40.68688 -73.95596
## room_type price minimum_nights number_of_reviews last_review
## 1 Private room 149 1 9 10/19/18
## 2 Entire home/apt 225 1 45 5/21/19
## 3 Entire home/apt 89 1 270 7/5/19
## 4 Entire home/apt 80 10 9 11/19/18
## 5 Entire home/apt 200 3 74 6/22/19
## 6 Private room 60 45 49 10/5/17
## reviews_per_month calculated_host_listings_count availability_365
## 1 0.21 6 365
## 2 0.38 2 355
## 3 4.64 1 194
## 4 0.10 1 0
## 5 0.59 1 129
## 6 0.40 1 0
## tsquare_distance
## 1 2.2968748
## 2 0.1459679
## 3 2.2596886
## 4 2.9737754
## 5 0.7525852
## 6 2.4536331Removing logically irrelevant variables
#Dropping logical irrelevant variables: "id", "name", "host_id", "host_name", "last_review", "latitude", "longitude", "neighborhood"
nyc2 <- select(nycraw, -c("id", "name", "host_id", "host_name", "last_review", "latitude", "longitude", "neighbourhood_group"))
head(nyc2)## neighbourhood room_type price minimum_nights
## 1 Kensington Private room 149 1
## 2 Midtown Entire home/apt 225 1
## 3 Clinton Hill Entire home/apt 89 1
## 4 East Harlem Entire home/apt 80 10
## 5 Murray Hill Entire home/apt 200 3
## 6 Bedford-Stuyvesant Private room 60 45
## number_of_reviews reviews_per_month calculated_host_listings_count
## 1 9 0.21 6
## 2 45 0.38 2
## 3 270 4.64 1
## 4 9 0.10 1
## 5 74 0.59 1
## 6 49 0.40 1
## availability_365 tsquare_distance
## 1 365 2.2968748
## 2 355 0.1459679
## 3 194 2.2596886
## 4 0 2.9737754
## 5 129 0.7525852
## 6 0 2.4536331Zero Value Variable Check
- Checking on dependent variable range to make sure if there are zero’s to remove. It would not be free to stay in NYC.
- Checking on independent variables that have ‘0’ as a value. Seeing that “availability_365” would mean the AirBnB isn’t available at all, we are dropping those from our data set.
nyc2 <- nyc2[!(nyc2$price==0),]
nyc2 <- nyc2[!(nyc2$availability_365==0),]
invisible(view(nyc2))NA Evaluation and Drop
#Checking for NAs
md.pattern(nyc2)## /\ /\
## { `---' }
## { O O }
## ==> V <== No need for mice. This data set is completely observed.
## \ \|/ /
## `-----'
## neighbourhood room_type price minimum_nights number_of_reviews
## 25487 1 1 1 1 1
## 0 0 0 0 0
## reviews_per_month calculated_host_listings_count availability_365
## 25487 1 1 1
## 0 0 0
## tsquare_distance
## 25487 1 0
## 0 0nrow(nyc2)## [1] 25487#Drop NAs that are present
nyc3 <- na.omit(nyc2)
#Confirming NA drop
nrow(nyc3)## [1] 25487Storing all categorical variables as factors
#Storing categorical variables as factors
skim(nyc3)## Skim summary statistics
## n obs: 25487
## n variables: 9
##
## ── Variable type:factor ──────────────────────────────────────────────────────────────────────────────────────────────────────────
## variable missing complete n n_unique
## neighbourhood 0 25487 25487 217
## room_type 0 25487 25487 3
## top_counts ordered
## Bed: 2172, Wil: 1739, Har: 1470, Bus: 1195 FALSE
## Ent: 13363, Pri: 11472, Sha: 652, NA: 0 FALSE
##
## ── Variable type:integer ─────────────────────────────────────────────────────────────────────────────────────────────────────────
## variable missing complete n mean sd p0
## availability_365 0 25487 25487 169.11 123.76 1
## calculated_host_listings_count 0 25487 25487 6.98 32.08 1
## minimum_nights 0 25487 25487 6.23 16.8 1
## number_of_reviews 0 25487 25487 38.94 54.8 1
## price 0 25487 25487 146.99 170.37 10
## p25 p50 p75 p100 hist
## 52 157 290 365 ▇▅▂▃▂▃▃▆
## 1 1 3 327 ▇▁▁▁▁▁▁▁
## 1 2 4 999 ▇▁▁▁▁▁▁▁
## 5 17 51 629 ▇▁▁▁▁▁▁▁
## 69 107 175 8500 ▇▁▁▁▁▁▁▁
##
## ── Variable type:numeric ─────────────────────────────────────────────────────────────────────────────────────────────────────────
## variable missing complete n mean sd p0 p25 p50 p75
## reviews_per_month 0 25487 25487 1.85 1.81 0.02 0.49 1.29 2.73
## tsquare_distance 0 25487 25487 3.44 3.07 0.016 1.48 2.69 4.26
## p100 hist
## 58.5 ▇▁▁▁▁▁▁▁
## 18.86 ▇▇▂▁▁▁▁▁Numerical v Numerical Multicollinearity
- Multicollinearity will weaken the model
- number_of_reviews and reviews_per_month are correlated at 55%
- Removing reviews_per_month
- number_of_reviews and reviews_per_month are correlated at 55%
corrNYC <- nyc3
#Table numeric variables
corrNYCTable <- corrNYC %>% keep(is.numeric) %>% cor %>% view
#Plot numeric variables v numeric variables
corrNYC %>% keep(is.numeric) %>% cor %>% corrplot("upper", addCoef.col = "white", number.digits = 2, number.cex = 0.5, method="square", order="hclust", tl.srt=45, tl.cex = 0.8)
invisible(view(corrNYCTable))#Removing reviews_per_month due to high correlation of is and number_of_reviews
nyc4 <- select(nyc3, -c("reviews_per_month"))Summary Review of Data Set
summary(nyc4)## neighbourhood room_type price
## Bedford-Stuyvesant: 2172 Entire home/apt:13363 Min. : 10
## Williamsburg : 1739 Private room :11472 1st Qu.: 69
## Harlem : 1470 Shared room : 652 Median : 107
## Bushwick : 1195 Mean : 147
## Hell's Kitchen : 1171 3rd Qu.: 175
## Upper East Side : 867 Max. :8500
## (Other) :16873
## minimum_nights number_of_reviews calculated_host_listings_count
## Min. : 1.000 Min. : 1.00 Min. : 1.000
## 1st Qu.: 1.000 1st Qu.: 5.00 1st Qu.: 1.000
## Median : 2.000 Median : 17.00 Median : 1.000
## Mean : 6.233 Mean : 38.94 Mean : 6.981
## 3rd Qu.: 4.000 3rd Qu.: 51.00 3rd Qu.: 3.000
## Max. :999.000 Max. :629.00 Max. :327.000
##
## availability_365 tsquare_distance
## Min. : 1.0 Min. : 0.01632
## 1st Qu.: 52.0 1st Qu.: 1.47596
## Median :157.0 Median : 2.69428
## Mean :169.1 Mean : 3.44215
## 3rd Qu.:290.0 3rd Qu.: 4.25571
## Max. :365.0 Max. :18.85560
## Changing Price variable range
nyc4 <- filter(nyc4, price >= 25 & price <= 400)Removing outliers from minimum nights stay
- Anything over 365 is more than a year and would be improbable
- Removing any minimum nights metric over 365
nyc4 <- nyc4[!(nyc4$minimum_nights > 365),]
invisible(view(nyc4))Reviewing Linearity with Numeric Variables
- Curved relationships with the numeric variables
- Could require a quadratic or logarithmic transformation
#nyc4 %>% pairs() No color model
pairs(nyc4,col=nyc4$neighbourhood) #Color by neighborhood
Creating new Log price variable
- Based on the above plots we may benefit from a transformation
- Log transforming price to create a log-linear regression
log.nyc <- nyc4 %>% mutate(lprice=log(price))
log.nyc <- select(log.nyc, -c("price"))
invisible(log.nyc)Reviewing Linearity with Log-Linear model: Independent and Logged Dependent (Price) Variable
- Curved relationships with the numeric variables
- Could require a quadratic or logarithmic transformation
pairs(log.nyc,col=log.nyc$neighbourhood)
Log-log model
- Due to lack of linearity trying to transform the independent variables to see if we can surface a linear relationship
log.indep.nyc <- log.nyc %>% mutate(lreviews=log(number_of_reviews))
log.indep.nyc <- log.indep.nyc %>% mutate(lnights=log(minimum_nights))
log.indep.nyc <- log.indep.nyc %>% mutate(llistings=log(calculated_host_listings_count))
log.indep.nyc <- log.indep.nyc %>% mutate(lavailablility=log(availability_365))
log.indep.nyc <- log.indep.nyc %>% mutate(ltsqr=log(tsquare_distance))
invisible(log.indep.nyc)
log.indep.nyc <- select(log.indep.nyc, -c("minimum_nights", "number_of_reviews", "calculated_host_listings_count", "availability_365", "tsquare_distance"))
# Checking for -inf logged results
invisible(log.indep.nyc)
# Drop -inf log reults in lavailability
log.indep.nyc<-log.indep.nyc[!(log.indep.nyc$lavailablility=="-Inf"),]
invisible(log.indep.nyc)Reviewing Linearity with Logged Independent and Dependent Variables
- Curved relationships with the numeric variables
- Could require a quadratic or logarithmic transformation
pairs(log.indep.nyc,col=log.indep.nyc$neighbourhood) #Color by neighborhood
Continuous Variable Bin Manipulation
- Since we are seeing large clouds of data but no linear trend with logged and unlogged data, we are going to move forward with binning the data to see if it will assist us in determining if there is a relationship between the continuous variables and log price
nyc.bins <- nyc4
nyc.bins$reviewsBin <- var.bin(nyc.bins$number_of_reviews, bins = 50)
nyc.bins$nightsBin <- var.bin(nyc.bins$minimum_nights, bins = 50)
nyc.bins$availBin <- var.bin(nyc.bins$availability_365, bins = 50)
nyc.bins$listBin <- var.bin(nyc.bins$calculated_host_listings_count, bins = 10)
nyc.bins$tsquBin <- var.bin(nyc.bins$tsquare_distance, bins = 20)
nyc.bins <- select(nyc.bins,-c("minimum_nights", "number_of_reviews", "calculated_host_listings_count", "availability_365", "tsquare_distance"))
invisible(nyc.bins)Reviewing Linearity with Binned Indepedent Variables
- No linearity is presenting itself with a binned approach of the independent variables
nyc.bin.model <-lm(price~.,data=nyc.bins)
#nyc.bins %>% pairs() No color model
pairs(nyc.bins,col=nyc.bins$neighbourhood) #Color by neighborhood
Explore potential correlation Neighborhood v Price
- We have to this moment not be able to surface linearity relationships between our numerican independent varaibles and our dependentt variable
- Next we will check for correltaion of the categorical variables: room_type & neighbourhood_group
- We see a strong chance of correlation between Price and Neighbourhood Group
plot(nyc4$neighbourhood, nyc4$price, xlab = "Neighbourhood", ylab = "Price", title = "Price v Neighbourhood Correlation Check", col=c(7,32,52,82,107)) 
- Narrowing down neighborhoods (randomly) to confirm neighbourhood is a significant categorical metrics to keep in MLR
nycNeighborhood <- ddply(nyc4,.(neighbourhood), function(x) x[sample(nrow(x),1),])
plot(nycNeighborhood$neighbourhood, nycNeighborhood$price, xlab = "Neighbourhood", ylab = "Price", title = "Price v Neighbourhood Correlation Check") 
Explore potential correlation Room Type v Price
- We see a strong chance of corerlation between Price and Room Type
plot(nyc4$room_type, nyc4$price, xlab = "Room Type", ylab = "Price", title = "Price v Room Type Correlation Check", col=c(7,32,52)) 
Modeling
- We are not seeing any linear correlation between the dependent and independent numeric varaibles
- We have tried: linear regression, log-linear regression transformation, log-log regression transformation, binning, and outlier drop.
- We are seeing a strong linear correlation between the dependent and independent categorical variables
- We have surfaced the best residuals assumptions matched in a log-linear model
- Due to these discoveries we are moving forward with a Two-Way ANOVA in order to create the strongest model
- The number of Neighborhoods is so high deriving any sort of practical significance in a two-way ANOVA would be too difficult.
- Changing our selected variables to Neighbourhod_Group and room_type
Clean data for Two-Way ANOVA
nyc.anova.raw <- read.csv("https://raw.githubusercontent.com/JaclynCoate/6372_Project/master/AB_NYC_2019.csv", header = TRUE, strip.white=TRUE)
head(nyc.anova.raw)## id name host_id
## 1 2539 Clean & quiet apt home by the park 2787
## 2 2595 Skylit Midtown Castle 2845
## 3 3831 Cozy Entire Floor of Brownstone 4869
## 4 5022 Entire Apt: Spacious Studio/Loft by central park 7192
## 5 5099 Large Cozy 1 BR Apartment In Midtown East 7322
## 6 5121 BlissArtsSpace! 7356
## host_name neighbourhood_group neighbourhood latitude longitude
## 1 John Brooklyn Kensington 40.64749 -73.97237
## 2 Jennifer Manhattan Midtown 40.75362 -73.98377
## 3 LisaRoxanne Brooklyn Clinton Hill 40.68514 -73.95976
## 4 Laura Manhattan East Harlem 40.79851 -73.94399
## 5 Chris Manhattan Murray Hill 40.74767 -73.97500
## 6 Garon Brooklyn Bedford-Stuyvesant 40.68688 -73.95596
## room_type price minimum_nights number_of_reviews last_review
## 1 Private room 149 1 9 10/19/18
## 2 Entire home/apt 225 1 45 5/21/19
## 3 Entire home/apt 89 1 270 7/5/19
## 4 Entire home/apt 80 10 9 11/19/18
## 5 Entire home/apt 200 3 74 6/22/19
## 6 Private room 60 45 49 10/5/17
## reviews_per_month calculated_host_listings_count availability_365
## 1 0.21 6 365
## 2 0.38 2 355
## 3 4.64 1 194
## 4 0.10 1 0
## 5 0.59 1 129
## 6 0.40 1 0nyc.anova.raw2 <- select(nyc.anova.raw, -c("id", "name", "host_id", "host_name", "last_review", "latitude", "longitude", "neighbourhood", "minimum_nights", "number_of_reviews", "last_review", "reviews_per_month", "calculated_host_listings_count", "availability_365"))
head(nyc.anova.raw2)## neighbourhood_group room_type price
## 1 Brooklyn Private room 149
## 2 Manhattan Entire home/apt 225
## 3 Brooklyn Entire home/apt 89
## 4 Manhattan Entire home/apt 80
## 5 Manhattan Entire home/apt 200
## 6 Brooklyn Private room 60nyc.anova.raw2 <- filter(nyc.anova.raw2, price >= 25 & price <= 400)
invisible(view(nyc.anova.raw2))Start 2-Way ANOVA Analysis
- In completing this project with the tools learned in Unit 3 - we will perform a 2-Way ANOVA analysis.
Summary Statistics Table
- Creating Mean, SD, SE, Min, Max, and IQR
- Table of graphable statistics
nyc.anova <- nyc.anova.raw2
#Attaching the data set
attach(nyc.anova)
#Creating a function
nycsummary<-function(x){
result<-c(length(x),mean(x),sd(x),sd(x)/sqrt(length(x)), min(x), max(x), IQR(x))
names(result)<-c("N","Mean","SD","SE","Min","Max","IQR")
return(result)
}
#Creating a summary stats table
nycsumstats<-aggregate(price~neighbourhood_group*room_type,data=nyc.anova,nycsummary)
nycsumstats<-cbind(nycsumstats[,1:2],nycsumstats[,-(1:2)])
nycsumstats## neighbourhood_group room_type N Mean SD SE
## 1 Bronx Entire home/apt 298 114.47987 58.13523 3.3676835
## 2 Brooklyn Entire home/apt 7019 154.03733 67.74270 0.8085835
## 3 Manhattan Entire home/apt 7940 190.24181 74.32768 0.8341427
## 4 Queens Entire home/apt 1594 135.40088 65.71060 1.6458538
## 5 Staten Island Entire home/apt 145 118.80000 58.50411 4.8585017
## 6 Bronx Private room 504 57.58929 26.98118 1.2018373
## 7 Brooklyn Private room 7002 70.03870 32.59757 0.3895599
## 8 Manhattan Private room 5455 99.57984 51.39588 0.6958745
## 9 Queens Private room 2538 64.01418 29.55717 0.5867012
## 10 Staten Island Private room 156 58.12179 27.52672 2.2039018
## 11 Bronx Shared room 35 42.68571 25.20244 4.2599900
## 12 Brooklyn Shared room 252 44.62302 29.90884 1.8840797
## 13 Manhattan Shared room 317 71.03470 40.11323 2.2529837
## 14 Queens Shared room 132 43.03030 19.56393 1.7028211
## 15 Staten Island Shared room 3 85.00000 60.62178 35.0000000
## Min Max IQR
## 1 35 399 51.00
## 2 25 400 85.00
## 3 35 400 97.25
## 4 25 400 70.00
## 5 48 300 65.00
## 6 25 300 28.00
## 7 25 400 30.00
## 8 25 400 46.00
## 9 25 395 28.00
## 10 25 235 33.00
## 11 25 165 22.50
## 12 25 250 15.00
## 13 25 350 31.00
## 14 25 120 15.00
## 15 30 150 60.00Summary Statistics Graph
#- The below graph shows characteristics of a nonadditive model #- Next Steps: # 1. Fit a non-additive model # 2. Check the assumptions # 3. Exmine Type III Sum of Squares F-test tables
ggplot(nycsumstats,aes(x=room_type,y=Mean,group=neighbourhood_group,colour=neighbourhood_group))+
ylab("NYC AirBnBs Prices")+xlab("Room Type")+
geom_line()+
geom_point()+
geom_errorbar(aes(ymin=Mean-SD,ymax=Mean+SD),width=.1)
Nonadditive 2-Way ANOVA
- QQ Plot for assumption assessment
- Show a curve, needs transformation
#The following code fits the nonadditive two way anova model and then produces the first the main residual diagnostics for assumption checking
nyc.model.fit<-aov(price~neighbourhood_group+room_type+neighbourhood_group:room_type,data=nyc.anova)
nyc.fits <- data.frame(fitted.values=nyc.model.fit$fitted.values,residuals=nyc.model.fit$residuals)
#Reisudals vs Fitted
nyc.plot1 <- ggplot(nyc.fits, aes(x=fitted.values,y=residuals))+ylab("Residuals")+
xlab("Predicted")+geom_point()
#QQ Plot of residuals #Note the diagonal abline is only good for qqplots of normal data
nyc.plot2 <- ggplot(nyc.fits,aes(sample=residuals))+
stat_qq()+geom_abline(intercept=mean(nyc.fits$residuals), slope = sd(nyc.fits$residuals))
#Histograms of residuals
nyc.plot3 <- ggplot(nyc.fits, aes(x=residuals)) +
geom_histogram(aes(y=..density..),binwidth=1,color="black", fill="gray")+
geom_density(alpha=.1, fill="red")
#Grid of all 3 graphs above
grid.arrange(nyc.plot1, nyc.plot2, nyc.plot3, ncol=3)
par(mfrow=c(2,2))
plot(nyc.model.fit)
Log transformation on price
#Transforming price to logged variable
nyc.log.anova <- nyc.anova %>% mutate(lprice=log(price))
#view(nyc.final)Assumptions check on log transformation of price
- Equal variances: there is some slight variation of variances but this will suffice in order to move forward
- QQ Plot: there is still some slight departure from normality, but again this is acceptable to move forward with our model
- DON’T FORGET TO MENTION CLT - Central Limit Theorum
nyc.model.fit.log<-aov(lprice~neighbourhood_group+room_type+neighbourhood_group:room_type,data=nyc.log.anova)
nyc.fits.log <- data.frame(fitted.values=nyc.model.fit.log$fitted.values,residuals=nyc.model.fit.log$residuals)
#Reisudals vs Fitted
nyc.logplot1 <- ggplot(nyc.fits.log, aes(x=fitted.values,y=residuals))+ylab("Residuals")+
xlab("Predicted")+geom_point()
#QQ Plot of residuals #Note the diagonal abline is only good for qqplots of normal data
nyc.logplot2 <- ggplot(nyc.fits.log,aes(sample=residuals))+
stat_qq()+geom_abline(intercept=mean(nyc.fits.log$residuals), slope = sd(nyc.fits.log$residuals))
#Histograms of residuals
nyc.logplot3 <- ggplot(nyc.fits.log, aes(x=residuals)) +
geom_histogram(aes(y=..density..),binwidth=1,color="black", fill="gray")+
geom_density(alpha=.1, fill="red")
#Grid of all 3 graphs above
grid.arrange(nyc.logplot1, nyc.logplot2, nyc.logplot3, ncol=3)
par(mfrow=c(2,2))
plot(nyc.model.fit.log)
Outliers
- Since there are not singular points that are aggressively skewing the data, these outliers aren’t considered unique or affecting the model in a way that would not be logical.
- Choose to leave all low and high end metrics since the model should take these into account
Type III F-test table
- From the below F-test table we can see that neighborhood_group, room_type, as well as their interaction are all statistically significant for this model
- The type-3 sums of squares F-test is provided below. The test for an interaction is not significant (F-stat: 12.493 p-value < .0001). Therefore, we can conclude that the potential changes in AirBnB price for one of the factors does depend on the other.
Anova(nyc.model.fit, type = 3)## Anova Table (Type III tests)
##
## Response: price
## Sum Sq Df F value
## (Intercept) 3905481 1 1187.124
## neighbourhood_group 8194094 4 622.677
## room_type 649678 2 98.739
## neighbourhood_group:room_type 529559 8 20.121
## Residuals 109799287 33375
## Pr(>F)
## (Intercept) < 0.00000000000000022 ***
## neighbourhood_group < 0.00000000000000022 ***
## room_type < 0.00000000000000022 ***
## neighbourhood_group:room_type < 0.00000000000000022 ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Anova(nyc.model.fit.log,type=3)## Anova Table (Type III tests)
##
## Response: lprice
## Sum Sq Df F value Pr(>F)
## (Intercept) 6420.9 1 39324.029 < 0.00000000000000022
## neighbourhood_group 350.2 4 536.194 < 0.00000000000000022
## room_type 93.4 2 286.105 < 0.00000000000000022
## neighbourhood_group:room_type 27.4 8 20.988 < 0.00000000000000022
## Residuals 5449.6 33375
##
## (Intercept) ***
## neighbourhood_group ***
## room_type ***
## neighbourhood_group:room_type ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Confidence Intervals for F Test
confint(nyc.model.fit.log)## 2.5 %
## (Intercept) 4.59597020
## neighbourhood_groupBrooklyn 0.26099010
## neighbourhood_groupManhattan 0.48444255
## neighbourhood_groupQueens 0.11454831
## neighbourhood_groupStaten Island -0.04476596
## room_typePrivate room -0.72145305
## room_typeShared room -1.13046074
## neighbourhood_groupBrooklyn:room_typePrivate room -0.17638784
## neighbourhood_groupManhattan:room_typePrivate room -0.06971507
## neighbourhood_groupQueens:room_typePrivate room -0.12053167
## neighbourhood_groupStaten Island:room_typePrivate room -0.14684224
## neighbourhood_groupBrooklyn:room_typeShared room -0.42930871
## neighbourhood_groupManhattan:room_typeShared room -0.17555003
## neighbourhood_groupQueens:room_typeShared room -0.28983872
## neighbourhood_groupStaten Island:room_typeShared room 0.07160305
## 97.5 %
## (Intercept) 4.687730749
## neighbourhood_groupBrooklyn 0.354678302
## neighbourhood_groupManhattan 0.577909184
## neighbourhood_groupQueens 0.214518934
## neighbourhood_groupStaten Island 0.115622772
## room_typePrivate room -0.605701211
## room_typeShared room -0.847423174
## neighbourhood_groupBrooklyn:room_typePrivate room -0.057584148
## neighbourhood_groupManhattan:room_typePrivate room 0.049341540
## neighbourhood_groupQueens:room_typePrivate room 0.005806175
## neighbourhood_groupStaten Island:room_typePrivate room 0.069461684
## neighbourhood_groupBrooklyn:room_typeShared room -0.128601673
## neighbourhood_groupManhattan:room_typeShared room 0.121673124
## neighbourhood_groupQueens:room_typeShared room 0.027483150
## neighbourhood_groupStaten Island:room_typeShared room 1.037936956Multiple Test Technique on No Transformation: Tukey-Kramer
- From the F-test table we can see that all current variables are statistically significnat at the 0.05 alpha level
- Move forward with the Tukey-Kramer to discover what factors and/or combinations contribute to predicting the price of a NYC AirBnB
nyc.anova.diff <- TukeyHSD(nyc.model.fit,"neighbourhood_group:room_type", conf.level = .95)
nyc.anova.diff## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = price ~ neighbourhood_group + room_type + neighbourhood_group:room_type, data = nyc.anova)
##
## $`neighbourhood_group:room_type`
## diff
## Brooklyn:Entire home/apt-Bronx:Entire home/apt 39.5574615
## Manhattan:Entire home/apt-Bronx:Entire home/apt 75.7619478
## Queens:Entire home/apt-Bronx:Entire home/apt 20.9210125
## Staten Island:Entire home/apt-Bronx:Entire home/apt 4.3201342
## Bronx:Private room-Bronx:Entire home/apt -56.8905801
## Brooklyn:Private room-Bronx:Entire home/apt -44.4411625
## Manhattan:Private room-Bronx:Entire home/apt -14.9000308
## Queens:Private room-Bronx:Entire home/apt -50.4656814
## Staten Island:Private room-Bronx:Entire home/apt -56.3580709
## Bronx:Shared room-Bronx:Entire home/apt -71.7941515
## Brooklyn:Shared room-Bronx:Entire home/apt -69.8568499
## Manhattan:Shared room-Bronx:Entire home/apt -43.4451655
## Queens:Shared room-Bronx:Entire home/apt -71.4495627
## Staten Island:Shared room-Bronx:Entire home/apt -29.4798658
## Manhattan:Entire home/apt-Brooklyn:Entire home/apt 36.2044863
## Queens:Entire home/apt-Brooklyn:Entire home/apt -18.6364490
## Staten Island:Entire home/apt-Brooklyn:Entire home/apt -35.2373273
## Bronx:Private room-Brooklyn:Entire home/apt -96.4480415
## Brooklyn:Private room-Brooklyn:Entire home/apt -83.9986240
## Manhattan:Private room-Brooklyn:Entire home/apt -54.4574922
## Queens:Private room-Brooklyn:Entire home/apt -90.0231429
## Staten Island:Private room-Brooklyn:Entire home/apt -95.9155324
## Bronx:Shared room-Brooklyn:Entire home/apt -111.3516130
## Brooklyn:Shared room-Brooklyn:Entire home/apt -109.4143114
## Manhattan:Shared room-Brooklyn:Entire home/apt -83.0026269
## Queens:Shared room-Brooklyn:Entire home/apt -111.0070242
## Staten Island:Shared room-Brooklyn:Entire home/apt -69.0373273
## Queens:Entire home/apt-Manhattan:Entire home/apt -54.8409353
## Staten Island:Entire home/apt-Manhattan:Entire home/apt -71.4418136
## Bronx:Private room-Manhattan:Entire home/apt -132.6525279
## Brooklyn:Private room-Manhattan:Entire home/apt -120.2031104
## Manhattan:Private room-Manhattan:Entire home/apt -90.6619786
## Queens:Private room-Manhattan:Entire home/apt -126.2276292
## Staten Island:Private room-Manhattan:Entire home/apt -132.1200187
## Bronx:Shared room-Manhattan:Entire home/apt -147.5560993
## Brooklyn:Shared room-Manhattan:Entire home/apt -145.6187977
## Manhattan:Shared room-Manhattan:Entire home/apt -119.2071133
## Queens:Shared room-Manhattan:Entire home/apt -147.2115106
## Staten Island:Shared room-Manhattan:Entire home/apt -105.2418136
## Staten Island:Entire home/apt-Queens:Entire home/apt -16.6008783
## Bronx:Private room-Queens:Entire home/apt -77.8115926
## Brooklyn:Private room-Queens:Entire home/apt -65.3621751
## Manhattan:Private room-Queens:Entire home/apt -35.8210433
## Queens:Private room-Queens:Entire home/apt -71.3866939
## Staten Island:Private room-Queens:Entire home/apt -77.2790834
## Bronx:Shared room-Queens:Entire home/apt -92.7151640
## Brooklyn:Shared room-Queens:Entire home/apt -90.7778624
## Manhattan:Shared room-Queens:Entire home/apt -64.3661780
## Queens:Shared room-Queens:Entire home/apt -92.3705753
## Staten Island:Shared room-Queens:Entire home/apt -50.4008783
## Bronx:Private room-Staten Island:Entire home/apt -61.2107143
## Brooklyn:Private room-Staten Island:Entire home/apt -48.7612968
## Manhattan:Private room-Staten Island:Entire home/apt -19.2201650
## Queens:Private room-Staten Island:Entire home/apt -54.7858156
## Staten Island:Private room-Staten Island:Entire home/apt -60.6782051
## Bronx:Shared room-Staten Island:Entire home/apt -76.1142857
## Brooklyn:Shared room-Staten Island:Entire home/apt -74.1769841
## Manhattan:Shared room-Staten Island:Entire home/apt -47.7652997
## Queens:Shared room-Staten Island:Entire home/apt -75.7696970
## Staten Island:Shared room-Staten Island:Entire home/apt -33.8000000
## Brooklyn:Private room-Bronx:Private room 12.4494175
## Manhattan:Private room-Bronx:Private room 41.9905493
## Queens:Private room-Bronx:Private room 6.4248987
## Staten Island:Private room-Bronx:Private room 0.5325092
## Bronx:Shared room-Bronx:Private room -14.9035714
## Brooklyn:Shared room-Bronx:Private room -12.9662698
## Manhattan:Shared room-Bronx:Private room 13.4454146
## Queens:Shared room-Bronx:Private room -14.5589827
## Staten Island:Shared room-Bronx:Private room 27.4107143
## Manhattan:Private room-Brooklyn:Private room 29.5411318
## Queens:Private room-Brooklyn:Private room -6.0245188
## Staten Island:Private room-Brooklyn:Private room -11.9169084
## Bronx:Shared room-Brooklyn:Private room -27.3529889
## Brooklyn:Shared room-Brooklyn:Private room -25.4156874
## Manhattan:Shared room-Brooklyn:Private room 0.9959971
## Queens:Shared room-Brooklyn:Private room -27.0084002
## Staten Island:Shared room-Brooklyn:Private room 14.9612968
## Queens:Private room-Manhattan:Private room -35.5656506
## Staten Island:Private room-Manhattan:Private room -41.4580401
## Bronx:Shared room-Manhattan:Private room -56.8941207
## Brooklyn:Shared room-Manhattan:Private room -54.9568191
## Manhattan:Shared room-Manhattan:Private room -28.5451347
## Queens:Shared room-Manhattan:Private room -56.5495320
## Staten Island:Shared room-Manhattan:Private room -14.5798350
## Staten Island:Private room-Queens:Private room -5.8923895
## Bronx:Shared room-Queens:Private room -21.3284701
## Brooklyn:Shared room-Queens:Private room -19.3911685
## Manhattan:Shared room-Queens:Private room 7.0205159
## Queens:Shared room-Queens:Private room -20.9838814
## Staten Island:Shared room-Queens:Private room 20.9858156
## Bronx:Shared room-Staten Island:Private room -15.4360806
## Brooklyn:Shared room-Staten Island:Private room -13.4987790
## Manhattan:Shared room-Staten Island:Private room 12.9129054
## Queens:Shared room-Staten Island:Private room -15.0914918
## Staten Island:Shared room-Staten Island:Private room 26.8782051
## Brooklyn:Shared room-Bronx:Shared room 1.9373016
## Manhattan:Shared room-Bronx:Shared room 28.3489860
## Queens:Shared room-Bronx:Shared room 0.3445887
## Staten Island:Shared room-Bronx:Shared room 42.3142857
## Manhattan:Shared room-Brooklyn:Shared room 26.4116844
## Queens:Shared room-Brooklyn:Shared room -1.5927128
## Staten Island:Shared room-Brooklyn:Shared room 40.3769841
## Queens:Shared room-Manhattan:Shared room -28.0043973
## Staten Island:Shared room-Manhattan:Shared room 13.9652997
## Staten Island:Shared room-Queens:Shared room 41.9696970
## lwr
## Brooklyn:Entire home/apt-Bronx:Entire home/apt 28.0529766
## Manhattan:Entire home/apt-Bronx:Entire home/apt 64.2846694
## Queens:Entire home/apt-Bronx:Entire home/apt 8.6450747
## Staten Island:Entire home/apt-Bronx:Entire home/apt -15.3748726
## Bronx:Private room-Bronx:Entire home/apt -71.1043797
## Brooklyn:Private room-Bronx:Entire home/apt -55.9462162
## Manhattan:Private room-Bronx:Entire home/apt -26.4714887
## Queens:Private room-Bronx:Entire home/apt -62.3766088
## Staten Island:Private room-Bronx:Entire home/apt -75.5803067
## Bronx:Shared room-Bronx:Entire home/apt -106.5498777
## Brooklyn:Shared room-Bronx:Entire home/apt -86.5032124
## Manhattan:Shared room-Bronx:Entire home/apt -59.1396190
## Queens:Shared room-Bronx:Entire home/apt -91.7864994
## Staten Island:Shared room-Bronx:Entire home/apt -142.3452835
## Manhattan:Entire home/apt-Brooklyn:Entire home/apt 33.0177230
## Queens:Entire home/apt-Brooklyn:Entire home/apt -24.0333176
## Staten Island:Entire home/apt-Brooklyn:Entire home/apt -51.5566665
## Bronx:Private room-Brooklyn:Entire home/apt -105.4179714
## Brooklyn:Private room-Brooklyn:Entire home/apt -87.2840163
## Manhattan:Private room-Brooklyn:Entire home/apt -57.9683584
## Queens:Private room-Brooklyn:Entire home/apt -94.5284434
## Staten Island:Private room-Brooklyn:Entire home/apt -111.6610680
## Bronx:Shared room-Brooklyn:Entire home/apt -144.3120142
## Brooklyn:Shared room-Brooklyn:Entire home/apt -121.8854350
## Manhattan:Shared room-Brooklyn:Entire home/apt -94.1714861
## Queens:Shared room-Brooklyn:Entire home/apt -128.0955740
## Staten Island:Shared room-Brooklyn:Entire home/apt -181.3628812
## Queens:Entire home/apt-Manhattan:Entire home/apt -60.1795622
## Staten Island:Entire home/apt-Manhattan:Entire home/apt -87.7419848
## Bronx:Private room-Manhattan:Entire home/apt -141.5875370
## Brooklyn:Private room-Manhattan:Entire home/apt -123.3919264
## Manhattan:Private room-Manhattan:Entire home/apt -94.0826404
## Queens:Private room-Manhattan:Entire home/apt -130.6629960
## Staten Island:Private room-Manhattan:Entire home/apt -147.8456868
## Bronx:Shared room-Manhattan:Entire home/apt -180.5070142
## Brooklyn:Shared room-Manhattan:Entire home/apt -158.0648281
## Manhattan:Shared room-Manhattan:Entire home/apt -130.3479463
## Queens:Shared room-Manhattan:Entire home/apt -164.2817560
## Staten Island:Shared room-Manhattan:Entire home/apt -217.5645843
## Staten Island:Entire home/apt-Queens:Entire home/apt -33.4729354
## Bronx:Private room-Queens:Entire home/apt -87.7516689
## Brooklyn:Private room-Queens:Entire home/apt -70.7602561
## Manhattan:Private room-Queens:Entire home/apt -41.3592431
## Queens:Private room-Queens:Entire home/apt -77.6030601
## Staten Island:Private room-Queens:Entire home/apt -93.5967844
## Bronx:Shared room-Queens:Entire home/apt -125.9526959
## Brooklyn:Shared room-Queens:Entire home/apt -103.9640067
## Manhattan:Shared room-Queens:Entire home/apt -76.3281549
## Queens:Shared room-Queens:Entire home/apt -109.9877263
## Staten Island:Shared room-Queens:Entire home/apt -162.8080647
## Bronx:Private room-Staten Island:Entire home/apt -79.5410105
## Brooklyn:Private room-Staten Island:Entire home/apt -65.0810370
## Manhattan:Private room-Staten Island:Entire home/apt -35.5867865
## Queens:Private room-Staten Island:Entire home/apt -71.3941825
## Staten Island:Private room-Staten Island:Entire home/apt -83.1161643
## Bronx:Shared room-Staten Island:Entire home/apt -112.7466234
## Brooklyn:Shared room-Staten Island:Entire home/apt -94.4518219
## Manhattan:Shared room-Staten Island:Entire home/apt -67.2661595
## Queens:Shared room-Staten Island:Entire home/apt -99.1696682
## Staten Island:Shared room-Staten Island:Entire home/apt -147.2573497
## Brooklyn:Private room-Bronx:Private room 3.4787582
## Manhattan:Private room-Bronx:Private room 32.9348821
## Queens:Private room-Bronx:Private room -3.0607041
## Staten Island:Private room-Bronx:Private room -17.2888493
## Bronx:Shared room-Bronx:Private room -48.9045563
## Brooklyn:Shared room-Bronx:Private room -27.9731966
## Manhattan:Shared room-Bronx:Private room -0.4981266
## Queens:Shared room-Bronx:Private room -33.5773280
## Staten Island:Shared room-Bronx:Private room -85.2245777
## Manhattan:Private room-Brooklyn:Private room 26.0284023
## Queens:Private room-Brooklyn:Private room -10.5312716
## Staten Island:Private room-Brooklyn:Private room -27.6628595
## Bronx:Shared room-Brooklyn:Private room -60.3135887
## Brooklyn:Shared room-Brooklyn:Private room -37.8873357
## Manhattan:Shared room-Brooklyn:Private room -10.1734479
## Queens:Shared room-Brooklyn:Private room -44.0973329
## Staten Island:Shared room-Brooklyn:Private room -97.3643154
## Queens:Private room-Manhattan:Private room -40.2393215
## Staten Island:Private room-Manhattan:Private room -57.2525758
## Bronx:Shared room-Manhattan:Private room -89.8779579
## Brooklyn:Shared room-Manhattan:Private room -67.4897514
## Manhattan:Shared room-Manhattan:Private room -39.7829673
## Queens:Shared room-Manhattan:Private room -73.6832414
## Staten Island:Shared room-Manhattan:Private room -126.9122682
## Staten Island:Private room-Queens:Private room -21.9372924
## Bronx:Shared room-Queens:Private room -54.4329270
## Brooklyn:Shared room-Queens:Private room -32.2381893
## Manhattan:Shared room-Queens:Private room -4.5665645
## Queens:Shared room-Queens:Private room -38.3486604
## Staten Island:Shared room-Queens:Private room -91.3820939
## Bronx:Shared room-Staten Island:Private room -51.8164217
## Brooklyn:Shared room-Staten Island:Private room -33.3146843
## Manhattan:Shared room-Staten Island:Private room -6.1103590
## Queens:Shared room-Staten Island:Private room -38.0949635
## Staten Island:Shared room-Staten Island:Private room -86.4980324
## Brooklyn:Shared room-Bronx:Shared room -33.1502497
## Manhattan:Shared room-Bronx:Shared room -6.2970923
## Queens:Shared room-Bronx:Shared room -36.6368372
## Staten Island:Shared room-Bronx:Shared room -74.7012577
## Manhattan:Shared room-Brooklyn:Shared room 9.9954844
## Queens:Shared room-Brooklyn:Shared room -22.4916780
## Staten Island:Shared room-Brooklyn:Shared room -72.5910568
## Queens:Shared room-Manhattan:Shared room -48.1533733
## Staten Island:Shared room-Manhattan:Shared room -98.8664014
## Staten Island:Shared room-Queens:Shared room -71.6008445
## upr
## Brooklyn:Entire home/apt-Bronx:Entire home/apt 51.0619464
## Manhattan:Entire home/apt-Bronx:Entire home/apt 87.2392262
## Queens:Entire home/apt-Bronx:Entire home/apt 33.1969504
## Staten Island:Entire home/apt-Bronx:Entire home/apt 24.0151410
## Bronx:Private room-Bronx:Entire home/apt -42.6767804
## Brooklyn:Private room-Bronx:Entire home/apt -32.9361088
## Manhattan:Private room-Bronx:Entire home/apt -3.3285728
## Queens:Private room-Bronx:Entire home/apt -38.5547540
## Staten Island:Private room-Bronx:Entire home/apt -37.1358351
## Bronx:Shared room-Bronx:Entire home/apt -37.0384253
## Brooklyn:Shared room-Bronx:Entire home/apt -53.2104874
## Manhattan:Shared room-Bronx:Entire home/apt -27.7507119
## Queens:Shared room-Bronx:Entire home/apt -51.1126261
## Staten Island:Shared room-Bronx:Entire home/apt 83.3855520
## Manhattan:Entire home/apt-Brooklyn:Entire home/apt 39.3912497
## Queens:Entire home/apt-Brooklyn:Entire home/apt -13.2395803
## Staten Island:Entire home/apt-Brooklyn:Entire home/apt -18.9179880
## Bronx:Private room-Brooklyn:Entire home/apt -87.4781117
## Brooklyn:Private room-Brooklyn:Entire home/apt -80.7132318
## Manhattan:Private room-Brooklyn:Entire home/apt -50.9466261
## Queens:Private room-Brooklyn:Entire home/apt -85.5178423
## Staten Island:Private room-Brooklyn:Entire home/apt -80.1699968
## Bronx:Shared room-Brooklyn:Entire home/apt -78.3912118
## Brooklyn:Shared room-Brooklyn:Entire home/apt -96.9431877
## Manhattan:Shared room-Brooklyn:Entire home/apt -71.8337678
## Queens:Shared room-Brooklyn:Entire home/apt -93.9184745
## Staten Island:Shared room-Brooklyn:Entire home/apt 43.2882267
## Queens:Entire home/apt-Manhattan:Entire home/apt -49.5023084
## Staten Island:Entire home/apt-Manhattan:Entire home/apt -55.1416424
## Bronx:Private room-Manhattan:Entire home/apt -123.7175188
## Brooklyn:Private room-Manhattan:Entire home/apt -117.0142943
## Manhattan:Private room-Manhattan:Entire home/apt -87.2413168
## Queens:Private room-Manhattan:Entire home/apt -121.7922624
## Staten Island:Private room-Manhattan:Entire home/apt -116.3943507
## Bronx:Shared room-Manhattan:Entire home/apt -114.6051844
## Brooklyn:Shared room-Manhattan:Entire home/apt -133.1727674
## Manhattan:Shared room-Manhattan:Entire home/apt -108.0662803
## Queens:Shared room-Manhattan:Entire home/apt -130.1412652
## Staten Island:Shared room-Manhattan:Entire home/apt 7.0809571
## Staten Island:Entire home/apt-Queens:Entire home/apt 0.2711788
## Bronx:Private room-Queens:Entire home/apt -67.8715162
## Brooklyn:Private room-Queens:Entire home/apt -59.9640941
## Manhattan:Private room-Queens:Entire home/apt -30.2828434
## Queens:Private room-Queens:Entire home/apt -65.1703276
## Staten Island:Private room-Queens:Entire home/apt -60.9613824
## Bronx:Shared room-Queens:Entire home/apt -59.4776322
## Brooklyn:Shared room-Queens:Entire home/apt -77.5917181
## Manhattan:Shared room-Queens:Entire home/apt -52.4042011
## Queens:Shared room-Queens:Entire home/apt -74.7534243
## Staten Island:Shared room-Queens:Entire home/apt 62.0063081
## Bronx:Private room-Staten Island:Entire home/apt -42.8804180
## Brooklyn:Private room-Staten Island:Entire home/apt -32.4415565
## Manhattan:Private room-Staten Island:Entire home/apt -2.8535434
## Queens:Private room-Staten Island:Entire home/apt -38.1774487
## Staten Island:Private room-Staten Island:Entire home/apt -38.2402460
## Bronx:Shared room-Staten Island:Entire home/apt -39.4819480
## Brooklyn:Shared room-Staten Island:Entire home/apt -53.9021464
## Manhattan:Shared room-Staten Island:Entire home/apt -28.2644399
## Queens:Shared room-Staten Island:Entire home/apt -52.3697258
## Staten Island:Shared room-Staten Island:Entire home/apt 79.6573497
## Brooklyn:Private room-Bronx:Private room 21.4200768
## Manhattan:Private room-Bronx:Private room 51.0462165
## Queens:Private room-Bronx:Private room 15.9105014
## Staten Island:Private room-Bronx:Private room 18.3538676
## Bronx:Shared room-Bronx:Private room 19.0974135
## Brooklyn:Shared room-Bronx:Private room 2.0406570
## Manhattan:Shared room-Bronx:Private room 27.3889558
## Queens:Shared room-Bronx:Private room 4.4593627
## Staten Island:Shared room-Bronx:Private room 140.0460063
## Manhattan:Private room-Brooklyn:Private room 33.0538613
## Queens:Private room-Brooklyn:Private room -1.5177661
## Staten Island:Private room-Brooklyn:Private room 3.8290428
## Bronx:Shared room-Brooklyn:Private room 5.6076108
## Brooklyn:Shared room-Brooklyn:Private room -12.9440390
## Manhattan:Shared room-Brooklyn:Private room 12.1654421
## Queens:Shared room-Brooklyn:Private room -9.9194675
## Staten Island:Shared room-Brooklyn:Private room 127.2869090
## Queens:Private room-Manhattan:Private room -30.8919797
## Staten Island:Private room-Manhattan:Private room -25.6635045
## Bronx:Shared room-Manhattan:Private room -23.9102836
## Brooklyn:Shared room-Manhattan:Private room -42.4238868
## Manhattan:Shared room-Manhattan:Private room -17.3073021
## Queens:Shared room-Manhattan:Private room -39.4158225
## Staten Island:Shared room-Manhattan:Private room 97.7525981
## Staten Island:Private room-Queens:Private room 10.1525134
## Bronx:Shared room-Queens:Private room 11.7759868
## Brooklyn:Shared room-Queens:Private room -6.5441477
## Manhattan:Shared room-Queens:Private room 18.6075963
## Queens:Shared room-Queens:Private room -3.6191023
## Staten Island:Shared room-Queens:Private room 133.3537251
## Bronx:Shared room-Staten Island:Private room 20.9442606
## Brooklyn:Shared room-Staten Island:Private room 6.3171263
## Manhattan:Shared room-Staten Island:Private room 31.9361699
## Queens:Shared room-Staten Island:Private room 7.9119798
## Staten Island:Shared room-Staten Island:Private room 140.2544427
## Brooklyn:Shared room-Bronx:Shared room 37.0248529
## Manhattan:Shared room-Bronx:Shared room 62.9950644
## Queens:Shared room-Bronx:Shared room 37.3260147
## Staten Island:Shared room-Bronx:Shared room 159.3298291
## Manhattan:Shared room-Brooklyn:Shared room 42.8278845
## Queens:Shared room-Brooklyn:Shared room 19.3062523
## Staten Island:Shared room-Brooklyn:Shared room 153.3450251
## Queens:Shared room-Manhattan:Shared room -7.8554213
## Staten Island:Shared room-Manhattan:Shared room 126.7970008
## Staten Island:Shared room-Queens:Shared room 155.5402384
## p adj
## Brooklyn:Entire home/apt-Bronx:Entire home/apt 0.0000000
## Manhattan:Entire home/apt-Bronx:Entire home/apt 0.0000000
## Queens:Entire home/apt-Bronx:Entire home/apt 0.0000008
## Staten Island:Entire home/apt-Bronx:Entire home/apt 0.9999901
## Bronx:Private room-Bronx:Entire home/apt 0.0000000
## Brooklyn:Private room-Bronx:Entire home/apt 0.0000000
## Manhattan:Private room-Bronx:Entire home/apt 0.0012031
## Queens:Private room-Bronx:Entire home/apt 0.0000000
## Staten Island:Private room-Bronx:Entire home/apt 0.0000000
## Bronx:Shared room-Bronx:Entire home/apt 0.0000000
## Brooklyn:Shared room-Bronx:Entire home/apt 0.0000000
## Manhattan:Shared room-Bronx:Entire home/apt 0.0000000
## Queens:Shared room-Bronx:Entire home/apt 0.0000000
## Staten Island:Shared room-Bronx:Entire home/apt 0.9999147
## Manhattan:Entire home/apt-Brooklyn:Entire home/apt 0.0000000
## Queens:Entire home/apt-Brooklyn:Entire home/apt 0.0000000
## Staten Island:Entire home/apt-Brooklyn:Entire home/apt 0.0000000
## Bronx:Private room-Brooklyn:Entire home/apt 0.0000000
## Brooklyn:Private room-Brooklyn:Entire home/apt 0.0000000
## Manhattan:Private room-Brooklyn:Entire home/apt 0.0000000
## Queens:Private room-Brooklyn:Entire home/apt 0.0000000
## Staten Island:Private room-Brooklyn:Entire home/apt 0.0000000
## Bronx:Shared room-Brooklyn:Entire home/apt 0.0000000
## Brooklyn:Shared room-Brooklyn:Entire home/apt 0.0000000
## Manhattan:Shared room-Brooklyn:Entire home/apt 0.0000000
## Queens:Shared room-Brooklyn:Entire home/apt 0.0000000
## Staten Island:Shared room-Brooklyn:Entire home/apt 0.7457561
## Queens:Entire home/apt-Manhattan:Entire home/apt 0.0000000
## Staten Island:Entire home/apt-Manhattan:Entire home/apt 0.0000000
## Bronx:Private room-Manhattan:Entire home/apt 0.0000000
## Brooklyn:Private room-Manhattan:Entire home/apt 0.0000000
## Manhattan:Private room-Manhattan:Entire home/apt 0.0000000
## Queens:Private room-Manhattan:Entire home/apt 0.0000000
## Staten Island:Private room-Manhattan:Entire home/apt 0.0000000
## Bronx:Shared room-Manhattan:Entire home/apt 0.0000000
## Brooklyn:Shared room-Manhattan:Entire home/apt 0.0000000
## Manhattan:Shared room-Manhattan:Entire home/apt 0.0000000
## Queens:Shared room-Manhattan:Entire home/apt 0.0000000
## Staten Island:Shared room-Manhattan:Entire home/apt 0.0949816
## Staten Island:Entire home/apt-Queens:Entire home/apt 0.0592759
## Bronx:Private room-Queens:Entire home/apt 0.0000000
## Brooklyn:Private room-Queens:Entire home/apt 0.0000000
## Manhattan:Private room-Queens:Entire home/apt 0.0000000
## Queens:Private room-Queens:Entire home/apt 0.0000000
## Staten Island:Private room-Queens:Entire home/apt 0.0000000
## Bronx:Shared room-Queens:Entire home/apt 0.0000000
## Brooklyn:Shared room-Queens:Entire home/apt 0.0000000
## Manhattan:Shared room-Queens:Entire home/apt 0.0000000
## Queens:Shared room-Queens:Entire home/apt 0.0000000
## Staten Island:Shared room-Queens:Entire home/apt 0.9734952
## Bronx:Private room-Staten Island:Entire home/apt 0.0000000
## Brooklyn:Private room-Staten Island:Entire home/apt 0.0000000
## Manhattan:Private room-Staten Island:Entire home/apt 0.0060403
## Queens:Private room-Staten Island:Entire home/apt 0.0000000
## Staten Island:Private room-Staten Island:Entire home/apt 0.0000000
## Bronx:Shared room-Staten Island:Entire home/apt 0.0000000
## Brooklyn:Shared room-Staten Island:Entire home/apt 0.0000000
## Manhattan:Shared room-Staten Island:Entire home/apt 0.0000000
## Queens:Shared room-Staten Island:Entire home/apt 0.0000000
## Staten Island:Shared room-Staten Island:Entire home/apt 0.9995992
## Brooklyn:Private room-Bronx:Private room 0.0002505
## Manhattan:Private room-Bronx:Private room 0.0000000
## Queens:Private room-Bronx:Private room 0.5927958
## Staten Island:Private room-Bronx:Private room 1.0000000
## Bronx:Shared room-Bronx:Private room 0.9783119
## Brooklyn:Shared room-Bronx:Private room 0.1823186
## Manhattan:Shared room-Bronx:Private room 0.0725456
## Queens:Shared room-Bronx:Private room 0.3722557
## Staten Island:Shared room-Bronx:Private room 0.9999639
## Manhattan:Private room-Brooklyn:Private room 0.0000000
## Queens:Private room-Brooklyn:Private room 0.0005663
## Staten Island:Private room-Brooklyn:Private room 0.3926501
## Bronx:Shared room-Brooklyn:Private room 0.2388147
## Brooklyn:Shared room-Brooklyn:Private room 0.0000000
## Manhattan:Shared room-Brooklyn:Private room 1.0000000
## Queens:Shared room-Brooklyn:Private room 0.0000086
## Staten Island:Shared room-Brooklyn:Private room 1.0000000
## Queens:Private room-Manhattan:Private room 0.0000000
## Staten Island:Private room-Manhattan:Private room 0.0000000
## Bronx:Shared room-Manhattan:Private room 0.0000005
## Brooklyn:Shared room-Manhattan:Private room 0.0000000
## Manhattan:Shared room-Manhattan:Private room 0.0000000
## Queens:Shared room-Manhattan:Private room 0.0000000
## Staten Island:Shared room-Manhattan:Private room 1.0000000
## Staten Island:Private room-Queens:Private room 0.9960658
## Bronx:Shared room-Queens:Private room 0.6759396
## Brooklyn:Shared room-Queens:Private room 0.0000314
## Manhattan:Shared room-Queens:Private room 0.7650326
## Queens:Shared room-Queens:Private room 0.0037890
## Staten Island:Shared room-Queens:Private room 0.9999987
## Bronx:Shared room-Staten Island:Private room 0.9838607
## Brooklyn:Shared room-Staten Island:Private room 0.5828455
## Manhattan:Shared room-Staten Island:Private room 0.5890421
## Queens:Shared room-Staten Island:Private room 0.6467812
## Staten Island:Shared room-Staten Island:Private room 0.9999738
## Brooklyn:Shared room-Bronx:Shared room 1.0000000
## Manhattan:Shared room-Bronx:Shared room 0.2603998
## Queens:Shared room-Bronx:Shared room 1.0000000
## Staten Island:Shared room-Bronx:Shared room 0.9966469
## Manhattan:Shared room-Brooklyn:Shared room 0.0000050
## Queens:Shared room-Brooklyn:Shared room 1.0000000
## Staten Island:Shared room-Brooklyn:Shared room 0.9970310
## Queens:Shared room-Manhattan:Shared room 0.0002421
## Staten Island:Shared room-Manhattan:Shared room 1.0000000
## Staten Island:Shared room-Queens:Shared room 0.9958048plot(TukeyHSD(nyc.model.fit,"neighbourhood_group:room_type", conf.level = .95))
nyc.anova.diff2 = tidy(nyc.anova.diff)
colnames(nyc.anova.diff2)[3] <- "diff"
invisible(view(nyc.anova.diff2))
nyc.anova.diffdf <- nyc.anova.diff2[nyc.anova.diff2$adj.p.value <0.05,]
nyc.anova.diffdf <- nyc.anova.diffdf[order(nyc.anova.diffdf$diff),]
nyc.anova.diffdf## # A tibble: 69 x 6
## term comparison diff conf.low conf.high adj.p.value
## <chr> <chr> <dbl> <dbl> <dbl> <dbl>
## 1 neighbourho… Bronx:Shared room-Man… -148. -181. -115. 0
## 2 neighbourho… Queens:Shared room-Ma… -147. -164. -130. 0
## 3 neighbourho… Brooklyn:Shared room-… -146. -158. -133. 0
## 4 neighbourho… Bronx:Private room-Ma… -133. -142. -124. 0
## 5 neighbourho… Staten Island:Private… -132. -148. -116. 0
## 6 neighbourho… Queens:Private room-M… -126. -131. -122. 0
## 7 neighbourho… Brooklyn:Private room… -120. -123. -117. 0
## 8 neighbourho… Manhattan:Shared room… -119. -130. -108. 0
## 9 neighbourho… Bronx:Shared room-Bro… -111. -144. -78.4 0
## 10 neighbourho… Queens:Shared room-Br… -111. -128. -93.9 0
## # … with 59 more rowsMultiple Test Technique on Log Transformationl: Tukey-Kramer
- From the F-test table we can see that all current variables are statistically significnat at the 0.05 alpha level
- Move forward with the Tukey-Kramer to discover what factors and/or combinations contribute to predicting the price of a NYC AirBnB
#nyc.anova.log.diff <- TukeyHSD(nyc.model.fit.log,"neighbourhood_group:room_type", conf.level = .95)
#nyc.anova.log.diff#plot(TukeyHSD(nyc.model.fit.log,"neighbourhood_group:room_type", conf.level = .95))Back Transformation
- To keep the data easily interpretable we have moved our nyc.anova.diff results into a data frame and are now going to back transform the diff and upper and lower confidence interval results.
#nyc.anova.log.diff2 = tidy(nyc.anova.log.diff)
#colnames(nyc.anova.log.diff2)[3] <- "diff"
#invisible(view(nyc.anova.log.diff2))
#nyc.anova.log.diffdf <- nyc.anova.log.diff2[nyc.anova.log.diff2$adj.p.value <0.05,]
#invisible(yc.anova.log.diffdf)
#ConfInt_Diff_Backlog <- yc.anova.log.diffdf %>% mutate(Tdiff = exp(diff))
#ConfInt_Diff_Backlog <- ConfInt_Diff_Backlog %>% mutate(Tlow = exp(conf.low))
#ConfInt_Diff_Backlog <- ConfInt_Diff_Backlog %>% mutate(Thigh = exp(conf.high))
#ConfInt_Diff_Backlog <- select(ConfInt_Diff_Backlog, -c("diff", "conf.low", "conf.high"))
#ConfInt_Diff_Backlog <- ConfInt_Diff_Backlog[order(-ConfInt_Diff_Backlog$Tdiff),]
#ConfInt_Diff_Backlog